Find an equation of the line having the given slope 4 and containing the given point (6, 11).

In this problem, we use the concept of the point-slope form of the straight line to find the equation.

Answer: The equation in slope-intercept form of the line through the point (6, 11) with slope 4 is given as y = 4x - 13.

Let us see how we solve the problem in detail.

Explanation:

Let us consider a point on the line (x, y).

We know that given two points (\((x)_{1}\), \((y)_{1}\)) and (\((x)_{2}\), \((y)_{2}\)) the slope is given by,

Slope(m) = (\((y)_{2}\) - \((y)_{1}\)) / (\((x)_{2}\) - \((x)_{1}\))

Here, m = 4

Hence, slope of the line passing through the points (6, 11) and (x, y) is,

(y - 11) / (x - 6) = 4

y - 11 = 4(x - 6)

y = 4x - 24 + 11

y = 4x - 13

Thus, the equation in slope-intercept form of the line through the point (6, 11) with slope 4 is given as y = 4x - 13.